Servers are with Gandi - which has a hosting API. So... SMS gateway via some shared hosting I have had for ages. This calls a script which figures out which server I mean and uses the API to shut it down.
I did used to use Twilio until they dropped international text messaging etc.
A shared hosting account which has a free (5 credits a month) SMS gateway included - I think it is reselling txtlocal.co.uk (who look quite good, but I haven't gotten round to trying them out directly yet).
It was kinda thrown together in a few minutes after Twilio flaked :)
I have a similar system, but instead of a plain passcode, I have a (simple, and probably not very secure) hashing method that I can do in my head.
My message looks like this: <machine> <hashed passcode> <number>
The passcode is "hashed" with the number. When the server receives the message, it adds the number to a deny-list. That way, the number is only good for one use.
Also, the number has to conform to a certain pattern. I might change that to a pre-generated list of valid numbers, but for the moment, I can work out a valid number with pen and paper.
Not perfect but can work well as a line of defence.